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The effect of delamination size and location to buckling behavior of composite materials
Accepted Manuscript The effect of delamination size and location to buckling behavior of composite materials Galip İpek, Yusuf Arman, Abdullah Çelik PII:
S1359-8368(18)31113-2
DOI:
10.1016/j.compositesb.2018.08.009
Reference:
JCOMB 5839
To appear in:
Composites Part B
Received Date: 10 April 2018 Revised Date:
12 July 2018
Accepted Date: 2 August 2018
Please cite this article as: İpek G, Arman Y, Çelik A, The effect of delamination size and location to buckling behavior of composite materials, Composites Part B (2018), doi: 10.1016/ j.compositesb.2018.08.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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THE EFFECT OF DELAMINATION SIZE AND LOCATION TO BUCKLING BEHAVIOR OF COMPOSITE MATERIALS a ˙ Galip Ipek , Yusuf Arman b and Abdullah C ¸ elik
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Dokuz Eyl¨ ul University, Graduate School of Natural and Applied Sciences, Tınaztepe ˙ Campus, Buca, Izmir, Turkey
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Dokuz Eyl¨ ul University, Engineering Faculty, Department of Mechanical Engineering, ˙ Tınaztepe Campus, Buca, Izmir, Turkey Corresponding Author: Abdullah C ¸ elik E-mail: [email protected]
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Abstract
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In this study, the size and location of delamination effects to layered composites’ mechanical properties in buckling behavior are inspected experimentally. Composite plates were produced in accordance with the different dimensions of delaminations and the positions between the layers. These plates consist in delamination rates of a/L = 0.3, 0.5, 0.7 (a: Delamination width and L: Buckling length). The specimens were subjected to buckling tests with placed on its two edges, while the others are free. In the experiments two results are considered. First, we determined load-displacement graphs. Critical buckling loads (P cr) were determined from the obtained load-displacement graphs. Second, we acquire lateral displacements, which occurred with the effect of applied load in the delamination area in direction of plate thickness. By comparing P cr with each other, an optimum delamination dimension was determined for composite materials with delamination zones. In the applications, the negative effect on the mechanical properties due to delaminations can be seen, proportionally according to the delamination location. Keywords: Laminated composite, delamination, critical buckling load, lateral displacement.
Preprint submitted to Elsevier
August 6, 2018
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1. Introduction
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In recent years, composites are being used in many different fields. Layered composites are one of the most used composite kind in industry. There can be discontinuities due to various reasons (resistance differences between layers, pulsed loadings, and defects in production etc.). These discontinuities affect layered composites negatively. The geometry of discontinuities (delaminations), their amounts between layers and their positions have an impact on composite’s mechanical properties on many levels. This impact is always negative. Delaminations significantly reduce the strength of the composite structure. The presence of one or more delaminations lead to reduced load carrying capacity of the damaged structure. In addition, the problem with the stability of the structure (buckling) can occur in unexpected situations. Increasing the size of the delaminations reduce the load carrying capacity of the structure. The level of this buckling load depends on the size, location and shape of the delamination of the layered composite material. Many researchers have investigated the effect of delamination on the load carrying capacity of composite structures using experimental, analytical or numerical (finite element methods). Kim et al. [1] presented an analytical solution to predict delamination buckling and growth of a thin fiber reinforced-plastic (FRP) layer in laminated wood beams under bending. They derived displacement functions for a delaminated beam under four-point bending are derived based on a strengthof-materials approach. The displacement, rotation and the axial force acting at the delaminated layer are computed, based on the assumed displacement functions which are derived using boundary conditions and compatibility conditions. Nonlinear buckling analysis, using the finite element method, was used by Hyo-Jin and Chang-Sun [2]. The objective is to investigate the buckling and forward buckling behavior of delaminated unidirectional composite materials under uniaxial compression. Hwang and Liu [4] studied the buckling behavior under the uniaxial compression force of carbon-epoxy materials using the finite element method. Short et al. [5] studied that delaminations in flat and curved composite laminates subjected to compressive load with experimental and numerical. They manufactured glass fiber reinforced plastic test laminates containing artificial delaminations of different sizes and through-thickness positions. Arman [6] analysed numerically and experimentally the effect of a circular delamination around a circular hole of a composite plate produced from a woven fabric on P cr. In their 2
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experimental studies, they produced specimens with delamination and without delamination. Cappello and Tumino [7] examined the buckling and the post-buckling behavior of single-sided and cross-laminated layered composite plates with multiple delaminations. Ascione at al. [9] studied a mechanical model able to predict the local buckling of pultruded FRP thin-walled beams and columns, taking into account the shear deformability of composite materials. Their model is based on the individual analysis of the buckling of the components of the FRP profile, assumed as elastically restrained transversely isotropic plates. Ascione at al. [10] presented a study on buckling phenomena in pultruded Fiber Reinforced Polymer (FRP) beams, based on two mechanical models recently formulated by the authors with regard to composite thin-walled beams. They analyzed several design charts relative to the failure load of I beams, characterized by both narrow and wide flanges, as well as subject to different load conditions. Ascione at al. [11] analyzed buckling modes of pultruded Fiber Reinforced Polymer (FRP) beams. The buckling behavior of FRP pultruded T and C beams has been investigated by adopting mechanical models taking into account the shear deformability of composite materials. A discussion on the effects of the beam geometry and on the failure modes is presented. Ruan et al. [12] experimentally examined 3D measurements on the deformation process with the 3D-DIC optical method for evaluating the delamination buckling of the damaged composite laminate. They analyzed the delamination buckling behavior of the impacted laminated specimen by this optical method. Their experimental results confirmed the effectiveness of the optical measuring method in gaining a better understanding of the deformation characteristics of the specimen. Ascione at al. [13] investigated a geometrically non-linear one-dimensional model suitable for analyzing thin-walled fiber-reinforced polymer profiles, which accounts for the effect of manufacturing imperfections. They developed a proper tool to analyze the pre-buckling behavior of such beams, since current approaches based on two-dimensional finite element method analysis demand significant computational efforts to be applied to real structures. Gong et al. [8] studied an investigation of the buckling behaviour and resultant damage modes in delaminated composites subjected to four-point bending. The effect of delamination size and shape on buckling behaviour was investigated using circular and elliptical delaminations in thin beams under four-point bending. Juh´asz, Z. And Szekr´enyes [14] analyzed the buckling process of composite plates with through-the-width delamination and straight crack front applying uniaxial compression. They focused on the mixed mode buckling case, 3
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where the non-uniform distribution of the in-plane forces controls the occurrence of the buckling of the delaminated layers. The effects of different type of boundary conditions were analyzed in a numerical example. The length of the delamination was varied, and the local and global critical amplitudes were calculated which results in a stability map for the different boundary conditions. Ahna et al. [15] proposed the delamination area factor for GFRP (Glass Fiber Reinforced Plastic) drilling to quantify the practical delamination zone via digital imaging of the damage zone around the hole and by calculating the damage zone by pixel. The tests concluded that a higher drill feed rate reduced the delamination zone and the cutting speeds have no influence on the delamination zone. They emphasized that the proposed delamination area factor was more suitable and useful for delamination zone evaluation than the existing delamination factor. Pernice et al. [16] explored the transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, experimentally. The test method used promotes delamination growth initially along a 0/Θ ply interface, which eventually migrates to a neighboring Θ/0 ply interface. They tested specimens with Θ = 60◦ and 75◦ .the study established a correlation between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses. Kharghani [17] investigated the effects of different parameters of the composite laminate and delaminated area analytically under buckling load and compared the results with the three-dimensional finite element analysis. The results demonstrate the effects of different geometrical parameters of the delaminated area and thickness on the deflection of a composite laminate. Nikrad et al. [18] made a computational study on the compressive instability of composite plates with off-center delaminations. They emphasized that the presence of delamination not only decreases the P cr, but also, plays an essential role in the load carrying capacity of composite structures. K¨ollner et al. [19] presented an analytical framework which allows modeling the postbuckling response of composites without such limitation. They studied the well-known problem of a composite strut with a through-the-width delamination. Their study was done up to the state of loading where the failure occurs in form of unstable delamination growth. They subjected them to buckling tests and compared them with numerical analysis results. LeBlanc and Plante [20] studied the moisture effects on delamination toughness and growth rate in a carbon/epoxy composite subjected to mixed-mode loadings. They obtained an adverse effect of moisture on delamination growth under 4
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mixed-mode loadings from the fatigue tests. Existing delamination criteria and growth rate models were evaluated to determine which ones best predict delamination toughness and growth, respectively, at any given mixed-mode ratio. Cardoso at al. [21] reported and discussed the findings from an experimental investigation on the flexural-torsional buckling behavior of pultruded glass-fiber reinforced polymer (GFRP) angle columns. A detailed material characterization was carried out and signature curves (critical load x length) were obtained using a generalized beam theory (GBT) software for predicting critical loads. In the literature, investigations on the effect of delamination on buckling load were mostly made on single delaminated composite plates. In general, studies have examined the effects of delaminations on the buckling loads. However, in a few researches, displacements in direction of plate thickness were enquired. Due to this deficiency in the literature, in this study; the effects of the delaminations size and location on buckling behaviour of the layered composites’ are inspected experimentally. As a result of buckling experiment, load-displacement graphics were obtained. The critical buckling loads were calculated by loading displacement graph. Additionally, lateral displacements were measured by transducers. Exact lateral displacement values were decided while P cr occurred. Optimum size and location of a delamination were obtained by comparison of critical buckling loads and lateral displacement values. 2. Materials and Methods
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2.1. Producing of Composite Plates and Preparation of Test Samples Material preparation phases are; composite production, curing, measuring processes, marking, cutting. 300g/m2 (0/90) E-glass fiber fabric (woven) was used as fiber reinforcement material in the production of layered composite plates. The epoxy resin (Huntsman (Araldite LY 564) epoxy and hardener mixed at a ratio of 100 : 34) was used as the matrix material. Composite plate production was carried out by resin infusion method supported with vacuum as seen in Figure 1. Eight-layered woven glass fiber reinforced epoxy resin matrix composite plates were used as materials. The reinforcing materials (woven E-glass fiber fabric) were prepared with cutting to size. The fiber fabrics are placed on the separator film so as to be centered. During placement, the first five layers are placed on top of each other, and then strips prepared from 100 microns Teflon PTFE film are placed at regular 5
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Delamination Location and Size (a/L) 5 − 6th layer / 0.3 6 − 7th layer / 0.3 7 − 8th layer / 0.3 5 − 6th layer / 0.5 6 − 7th layer / 0.5 7 − 8th layer / 0.5 5 − 6th layer / 0.7 6 − 7th layer / 0.7 7 − 8th layer / 0.7
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Sample Number A1 A2 A3 B1 B2 B3 C1 C2 C3
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Figure 1: Resin infusion method supported with vacuum
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Table 1: Sample numbers, delamination dimensions and locations in the experiments.
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intervals to provide the delaminations related with sample types. Then an upper layer of woven fabric is placed. Delamination locations were changed between 5−6th , 6−7th and 7−8th layers. In addition, delamination size with a/L ratio of 0.3, 0.5 and 0.7 rates were preferred (a: Delamination width and L: Buckling length). A total of 45 tests were performed as 5 pieces for one parameter. These sample types were given in Table 2. The sample number, the delamination dimension and the position of the delamination used in the experiments are given in Table 2. As it can be seen in Figure 2, the regions labeled ”Clamped Area” (25 mm from both sides) are reserved for the built-in fixed end of boundary conditions. The rest sample size for the buckling test was obtained as 100 mm × 30 mm × 2.3 mm. 6
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Figure 2: Buckling test specimen dimensions
Figure 3: Shimadzu AG-X with linear variable displacement transducers
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2.2. Experimental Study In the experimental study, buckling tests were carried out on a Shimadzu AG-X tensile-compressive universal test device with a load capacity of 100 kN with lateral displacement transducers as shown in Figure 3. In our tests, standard tension-compression jaws belonging to the device were used. Since the buckling test, the compression module of the device was used. These tests were carried out with a pressing speed of 1 mm/min. In the experiments, 5 specimens specially prepared for each case to be investigated were used and averages of 5 tests were taken. P cr loads were determined from the loaddisplacement graphs obtained as a result of the buckling tests made for each sample. At the end of the test, the results were recorded to the computer automatically and this data has been used in the desired graphics. Figure 12 contains force-displacement and force-lateral displacement graphs. 7
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Figure 4: Force-displacement and force-lateral displacements graph of the A1 samples
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Figure 5: Force-displacement and force-lateral displacements graph of the A2 samples
Figure 6: Force-displacement and force-lateral displacements graph of the A3 samples
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Figure 7: Force-displacement and force-lateral displacements graph of the B1 samples
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Figure 8: Force-displacement and force-lateral displacements graph of the B2 samples
Figure 9: Force-displacement and force-lateral displacements graph of the B3 samples
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Figure 10: Force-displacement and force-lateral displacements graph of the C1 samples
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Figure 11: Force-displacement and force-lateral displacements graph of the C2 samples
Figure 12: Force-displacement and force-lateral displacements graph of the C3 samples
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Figure 13: Determination of the P cr
P cr (N ) 1273 991 686
Sample Number A2 B2 C2
P cr (N ) 1260 840 655
Sample Number A3 B3 C3
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Sample Number A1 B1 C1
P cr (N ) 811 774 628
Table 2: The square mean of the experimental critical buckling loads
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Using the force-displacement graphs above, the force-displacement P cr values, which are the force values corresponding to the points at which the curve of the graph has deviated from the linearity, have been determined as shown in Figure 13. Experimental studies in the literature reference recorded to determine this point. Juh´asz at al. studied the effect of delamination on the critical buckling force of composite plates and they obtained critical buckling loads in this study. [22] The critical buckling loads found are shown in Table 2. The values in the table are the square mean of the critical buckling loads of each sample.
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3. Results and Discussion P cr - Lateral displacement comparison was made with values which obtained from the critical buckling loads given in Table 2. P cr - Lateral displacement comparison is based on the lateral displacements in millimeters corresponding to the P cr values. Comparisons were made by matching these values to each other. Figure 14 shows the case where the delamination locations are displaced from the middle interface to the upper interface while the delamination ratio is a/L = 0.3. P cr was obtained as 1273 N for A1 11
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Figure 14: Comparison of P cr and Lateral Displacement with delamination replacement between Layers (a/L = 0.3); (a) P cr Comparison, (b) Lateral Displacement Comparison
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sample. P crs were obtained as 1260 N for A2 specimen and 811 N for the A3 specimen with delamination layer position change. Decreasing rate was obtained as 36% in the P cr damage load decreases while the delamination position changed from the center interface to the edge interface. When P cr is decreasing by changing the outward position of delaminations; the opposite is obtained in the lateral displacement comparisons. It was observed that the displacements of the delamination from the middle interface to the upper interface increased lateral displacement values from 0.197 mm to 0.4 mm. The lateral displacement from the middle interface to the edge interface of the delamination affected the lateral displacement value with 103% increasing rate. Through our empirical study, we obtain that the delaminations around the mid-plane of the composite plate deteriorate the compressive instability response and hasten the buckling failure and reduce substantially the stiffness of delaminated composite plates. In Nikrad et al. [18] same results were highlighted. Hence, transfer displacement of mid-plane delaminations has less value because of hastening the buckling failure. Figure 15 shows the case where the delamination locations are displaced from the middle interface to the upper interface while the delamination ratio is a/L = 0.5. P cr was resulted as 991 N for B1 sample. P crs were obtained as 840 N for B2 specimen and 774 N for the B3 specimen with delamination layer position change. Decreasing rate was provided as 22% in the P cr damage load decreases while the delamination position changed from the center interface to the edge interface . When P cr is decreasing by changing the outward position of delami-
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Figure 15: Comparison of P cr and Lateral Displacement with delamination replacement between Layers (a/L = 0.5); (a) P cr Comparison, (b) Lateral Displacement Comparison
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nations; the opposite is found in the lateral displacement comparisons. It was observed that the displacements of the delamination from the middle interface to the upper interface increased lateral displacement values from 0.242 mm to 0.408 mm. The lateral displacement from the middle interface to the edge interface of the delamination afected the lateral displacement value with 68% increasing rate. Gong et al. [8] studied an investigation of the buckling behavior and resultant damage modes in delaminated composites subjected to four-point bending. The effect of delamination size and shape on buckling behavior was investigated using circular and elliptical delaminations in thin beams under four-point bending. They showed the orientation of the delamination had a small influence (10 − 15%) on the critical delamination-buckling load, which decreased with increasing ratio of minor to major axis length of the delamination. Small delamination has no big influence on the failure mode of the composite laminate. As might be expected, the P cr decreased with increasing size of the delamination. Figure 16 shows the case where the delamination locations are displaced from the middle interface to the upper interface while the delamination ratio is a / L = 0.7. The maximum P cr was obtained as 686 N for C1 sample. P crs were obtained as 655 N for C2 specimen and 628 N for the C3 specimen with delamination layer position change. Decreasing rate was obtained as 8% in the P cr damage load decreases while the delamination position changed from the center interface to the edge interface. When P cr is decreasing by changing the outward position of delamina13
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Figure 16: Comparison of P cr and Lateral Displacement with delamination replacement between Layers (a/L = 0.7); (a) P cr Comparison, (b) Lateral Displacement Comparison
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Figure 17: Damage loads and lateral displacements in delamination size increase between 7th and 8th layers; (a) P cr Comparison, (b) Lateral Displacement Comparison
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tions; the opposite is performed in the lateral displacement comparisons. It was observed that the displacements of the delamination from the middle interface to the upper interface increased lateral displacement values from 0.25 mm to 0.588 mm. The lateral displacement from the middle interface to the edge interface of the delamination affected the lateral displacement value with 135% increasing rate. Short et al. [5] showed that a delamination near the outside of the curve gave a greater strength reduction than a delamination near the inside of the curve, where both delaminations were at the same depth in their study like this study. In Figure 17, P cr and lateral displacement comparisons are given with the increase of the delamination rate in the same layer. The maximum
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Figure 18: Damage loads and lateral displacements in delamination size increase between 6th and 7th layers; (a) P cr Comparison, (b) Lateral Displacement Comparison
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P cr was carried out as 811 N for A3 sample. P crs were achieved as 774 N for B3 specimen and 628 N for the C3 specimen with the increase of the delamination rate in the same layer. Decreasing rate was obtained as 22% in the P cr damage load decreases while the delamination position shifted from the middle interface to the edge interface. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. Lateral displacements measured as 0.4 mm for A3, as 0.408 for B3, as 0.588 for C3. It was observed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 47% increasing rate. In Figure 18, P cr and lateral displacement comparisons are given with the increase of the delamination rate in the same layer. The maximum P cr was performed as 1260 N for A2 sample. P crs were obtained as 840 N for B2 specimen and 655 N for the C2 specimen with the increase of the delamination rate in the same layer. Decreasing rate was obtained as 48% in the P cr damage load decreases while the delamination position shifted from the middle interface to the edge interface. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. Lateral displacements measured as 0.324 mm for A2, as 0.326 for B2, as 0.348 for C2. It was viewed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 7% increasing rate. In Figure 19, P cr and lateral displacement comparisons are given with the increase of the delamination rate in the same layer. The maximum P cr was found as 1273 N for A1 sample. P crs were seen as 991 N for B1 specimen and 686 N for the C1 specimen
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Figure 19: Damage loads and lateral displacements in delamination size increase between 5th and 6th layers; (a) P cr Comparison, (b) Lateral Displacement Comparison
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with the increase of the delamination rate in the same layer. Decreasing rate was 46% in the P cr damage load decreases while the delamination position shifted from the middle interface to the edge interface. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. Lateral displacements measured as 0.197 mm for A1, as 0.242 mm for B1, as 0.25 mm for C1. It was observed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 26% increasing rate. Gu and Chattopadhyay [3] obtained both the critical stress and the ultimate stress reduced as the delamination length increases. They obtained the same size delamination position change from center lay to surface face decreased P cr. Lateral deflection measured to get buckling points. 4. Conclusion
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In this study, the effect of delamination size and location to P cr and lateral displacement behavior of composite materials was investigated. The remarkable results obtained from experiments are presented below. 1. The increase in delamination size on the same layer decreased the critical buckling loads. 5−6th layer, 6−7th layer and 7−8th layer decreasing rate was obtained as 46%, 48% and 22% respectively in the P cr failure load decreases while the increase in delamination size on the same layer.
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2. Delaminations of the same size reduced the buckling loads by changing the position from the middle interface to the upper interface. 5 − 6th layer, 6 − 7th layer and 7 − 8th layer decreasing rate was obtained as 36%, 22% and 08% respectively while the P cr damage load decreases by changing the position from the middle interface to the upper interface. 3. The increase in delamination size on the same layer increased the lateral displacements corresponding to the buckling loads of the material. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. It was observed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 26% increasing rate. 4. The location of the delaminations from the middle interface to the upper interface increased lateral displacements corresponding to buckling loads. The lateral displacement from the middle interface to the edge interface of the delamination affected the lateral displacement value with 135%, 68% and 103% increasing rate respectively for a / L = 0.3, 0.5 and 0.7.
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[1] Kim, Y., Davalos,J., Barbero, E.,( 1997) Delamination buckling of FRP layer in laminated wood beams, Composite Structures Vol. 37, No. 314, pp. 311-320. [2] Hyo-Jin, K. ve Chang-Sun, H., (1997). Buckling and post buckling behavior of composite laminates with a delamination. Composites Science and Technology, 57: 557-564.
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[3] Gu, H., Chattopadhyay, A., An experimental investigation of delamination buckling and postbuckling of composite laminates, Composites Science and Technology 59 (1999) 903-910. [4] Hwang, S. ve Liu, G., (2001). Buckling behavior of composite laminates with multiple delaminastions under uniaxial compression. Composite Structures, 53: 235-243. [5] Short, G., Guild, F., Pavier, M., Delaminations in flat and curved composite laminates subjected to compressive load, Composite Structures 58 (2002) 249258.
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[6] Arman, Y., Zor, M., Aksoy, S., Determination of critical delamination diameter of laminated composite plates under buckling loads. Composites Science and Technology 66 (2006) 29452953. [7] Cappello, F. ve Tumino, D., (2006). Numerical analysis of composite plates with multiple delaminations subjected to uniaxial buckling load. Composites Science and Technology, 66: 264-72.
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[8] Gong, W., Chen, J., Patterson, E., An experimental study of the behaviour of delaminations in composite panels subjected to bending, Composite Structures 123 (2015) 918.
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[9] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Local buckling behavior of FRP thin-walled beams: A mechanical model, Composite Structures 98 (2013) 111-120. [10] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Buckling failure modes of FRP thin-walled beams: A mechanical model, Composites: Part B 47 (2013) 357-364.
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[11] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Macro-scale analysis of local and global buckling behaviorof T and C composite sections, Mechanics Research Communications 58 (2014) 105-111.
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[12] Ruan, J. T., Aymerich, F., Tong, J. W. and Wang, Z. Y., (2014). Optical evaluation on delamination buckling of composite laminate with mpact damage, Advances in Materials Science and Engineering, Volume 2014, Article ID 390965.
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[13] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Pre-buckling imperfection sensitivity of pultruded FRP profiles, Composites: Part B 72 (2015) 206212. [14] Juh´asz, Z. And Szekr´enyes, A., (2015). Estimation of local delamination buckling in orthotropic composite plates using kirchhoff plate finite elements, Mathematical Problems in Engineering, Volume 2015, Article ID 749607. [15] Ahna, D.,Choib, J., and Kweonb, J., Relationship between the drilling condition and the damage (delamination) zone of glass-fiber-reinforced
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plastic composites, Advanced Composite Materials, 2015, Vol. 24, No. 3, 297305. [16] Pernice, M., Carvalho, N., Ratcliffe, J., Hallett, S., Experimental study on delamination migration in composite laminates, Composites: Part A 73 (2015) 2034.
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[17] Kharghani, N., Soares, C., Behavior of composite laminates with embedded delaminations, Composite Structures 150 (2016) 226239.
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[18] Nikrad, S., Keypoursangsari, S., Asadi, H., Akbarzadeh, A., Chen, Z., Computational study on compressive instability of composite plates with off-center delaminations, ScienceDirect, Comput. Methods Appl. Mech. Engrg. 310 (2016) 429459. [19] K¨ollner, A., Jungnickel, R., and V¨ollmecke, C., (2016). Delamination growth in buckled composite struts, Springer Science+Business Media Dordrecht, Int J Fract (2016) 202:261269.
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[20] LeBlanc, L. and LaPlante, G., Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon/epoxy composite, Composites: Part A 81 (2016) 202213. [21] Cardoso, D.C.T., Togashi, B.S., Experimental investigation on the flexural-torsional buckling behavior of pultruded GFRP angle columns, Thin-Walled Structures 125 (2018) 269-280.
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[22] Juh´asz, Z. And Szekr´enyes, A., The effect of delamination on the critical buckling force of composite plates: Experiment and simulation, Composite Structures 168 (2017) 456464.
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S1359-8368(18)31113-2
DOI:
10.1016/j.compositesb.2018.08.009
Reference:
JCOMB 5839
To appear in:
Composites Part B
Received Date: 10 April 2018 Revised Date:
12 July 2018
Accepted Date: 2 August 2018
Please cite this article as: İpek G, Arman Y, Çelik A, The effect of delamination size and location to buckling behavior of composite materials, Composites Part B (2018), doi: 10.1016/ j.compositesb.2018.08.009. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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THE EFFECT OF DELAMINATION SIZE AND LOCATION TO BUCKLING BEHAVIOR OF COMPOSITE MATERIALS a ˙ Galip Ipek , Yusuf Arman b and Abdullah C ¸ elik
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Dokuz Eyl¨ ul University, Graduate School of Natural and Applied Sciences, Tınaztepe ˙ Campus, Buca, Izmir, Turkey
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Dokuz Eyl¨ ul University, Engineering Faculty, Department of Mechanical Engineering, ˙ Tınaztepe Campus, Buca, Izmir, Turkey Corresponding Author: Abdullah C ¸ elik E-mail: [email protected]
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Abstract
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In this study, the size and location of delamination effects to layered composites’ mechanical properties in buckling behavior are inspected experimentally. Composite plates were produced in accordance with the different dimensions of delaminations and the positions between the layers. These plates consist in delamination rates of a/L = 0.3, 0.5, 0.7 (a: Delamination width and L: Buckling length). The specimens were subjected to buckling tests with placed on its two edges, while the others are free. In the experiments two results are considered. First, we determined load-displacement graphs. Critical buckling loads (P cr) were determined from the obtained load-displacement graphs. Second, we acquire lateral displacements, which occurred with the effect of applied load in the delamination area in direction of plate thickness. By comparing P cr with each other, an optimum delamination dimension was determined for composite materials with delamination zones. In the applications, the negative effect on the mechanical properties due to delaminations can be seen, proportionally according to the delamination location. Keywords: Laminated composite, delamination, critical buckling load, lateral displacement.
Preprint submitted to Elsevier
August 6, 2018
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1. Introduction
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In recent years, composites are being used in many different fields. Layered composites are one of the most used composite kind in industry. There can be discontinuities due to various reasons (resistance differences between layers, pulsed loadings, and defects in production etc.). These discontinuities affect layered composites negatively. The geometry of discontinuities (delaminations), their amounts between layers and their positions have an impact on composite’s mechanical properties on many levels. This impact is always negative. Delaminations significantly reduce the strength of the composite structure. The presence of one or more delaminations lead to reduced load carrying capacity of the damaged structure. In addition, the problem with the stability of the structure (buckling) can occur in unexpected situations. Increasing the size of the delaminations reduce the load carrying capacity of the structure. The level of this buckling load depends on the size, location and shape of the delamination of the layered composite material. Many researchers have investigated the effect of delamination on the load carrying capacity of composite structures using experimental, analytical or numerical (finite element methods). Kim et al. [1] presented an analytical solution to predict delamination buckling and growth of a thin fiber reinforced-plastic (FRP) layer in laminated wood beams under bending. They derived displacement functions for a delaminated beam under four-point bending are derived based on a strengthof-materials approach. The displacement, rotation and the axial force acting at the delaminated layer are computed, based on the assumed displacement functions which are derived using boundary conditions and compatibility conditions. Nonlinear buckling analysis, using the finite element method, was used by Hyo-Jin and Chang-Sun [2]. The objective is to investigate the buckling and forward buckling behavior of delaminated unidirectional composite materials under uniaxial compression. Hwang and Liu [4] studied the buckling behavior under the uniaxial compression force of carbon-epoxy materials using the finite element method. Short et al. [5] studied that delaminations in flat and curved composite laminates subjected to compressive load with experimental and numerical. They manufactured glass fiber reinforced plastic test laminates containing artificial delaminations of different sizes and through-thickness positions. Arman [6] analysed numerically and experimentally the effect of a circular delamination around a circular hole of a composite plate produced from a woven fabric on P cr. In their 2
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experimental studies, they produced specimens with delamination and without delamination. Cappello and Tumino [7] examined the buckling and the post-buckling behavior of single-sided and cross-laminated layered composite plates with multiple delaminations. Ascione at al. [9] studied a mechanical model able to predict the local buckling of pultruded FRP thin-walled beams and columns, taking into account the shear deformability of composite materials. Their model is based on the individual analysis of the buckling of the components of the FRP profile, assumed as elastically restrained transversely isotropic plates. Ascione at al. [10] presented a study on buckling phenomena in pultruded Fiber Reinforced Polymer (FRP) beams, based on two mechanical models recently formulated by the authors with regard to composite thin-walled beams. They analyzed several design charts relative to the failure load of I beams, characterized by both narrow and wide flanges, as well as subject to different load conditions. Ascione at al. [11] analyzed buckling modes of pultruded Fiber Reinforced Polymer (FRP) beams. The buckling behavior of FRP pultruded T and C beams has been investigated by adopting mechanical models taking into account the shear deformability of composite materials. A discussion on the effects of the beam geometry and on the failure modes is presented. Ruan et al. [12] experimentally examined 3D measurements on the deformation process with the 3D-DIC optical method for evaluating the delamination buckling of the damaged composite laminate. They analyzed the delamination buckling behavior of the impacted laminated specimen by this optical method. Their experimental results confirmed the effectiveness of the optical measuring method in gaining a better understanding of the deformation characteristics of the specimen. Ascione at al. [13] investigated a geometrically non-linear one-dimensional model suitable for analyzing thin-walled fiber-reinforced polymer profiles, which accounts for the effect of manufacturing imperfections. They developed a proper tool to analyze the pre-buckling behavior of such beams, since current approaches based on two-dimensional finite element method analysis demand significant computational efforts to be applied to real structures. Gong et al. [8] studied an investigation of the buckling behaviour and resultant damage modes in delaminated composites subjected to four-point bending. The effect of delamination size and shape on buckling behaviour was investigated using circular and elliptical delaminations in thin beams under four-point bending. Juh´asz, Z. And Szekr´enyes [14] analyzed the buckling process of composite plates with through-the-width delamination and straight crack front applying uniaxial compression. They focused on the mixed mode buckling case, 3
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where the non-uniform distribution of the in-plane forces controls the occurrence of the buckling of the delaminated layers. The effects of different type of boundary conditions were analyzed in a numerical example. The length of the delamination was varied, and the local and global critical amplitudes were calculated which results in a stability map for the different boundary conditions. Ahna et al. [15] proposed the delamination area factor for GFRP (Glass Fiber Reinforced Plastic) drilling to quantify the practical delamination zone via digital imaging of the damage zone around the hole and by calculating the damage zone by pixel. The tests concluded that a higher drill feed rate reduced the delamination zone and the cutting speeds have no influence on the delamination zone. They emphasized that the proposed delamination area factor was more suitable and useful for delamination zone evaluation than the existing delamination factor. Pernice et al. [16] explored the transition of delamination growth between different ply interfaces in composite tape laminates, known as migration, experimentally. The test method used promotes delamination growth initially along a 0/Θ ply interface, which eventually migrates to a neighboring Θ/0 ply interface. They tested specimens with Θ = 60◦ and 75◦ .the study established a correlation between these experimental observations and the shear stress sign at the delamination front, obtained by finite element analyses. Kharghani [17] investigated the effects of different parameters of the composite laminate and delaminated area analytically under buckling load and compared the results with the three-dimensional finite element analysis. The results demonstrate the effects of different geometrical parameters of the delaminated area and thickness on the deflection of a composite laminate. Nikrad et al. [18] made a computational study on the compressive instability of composite plates with off-center delaminations. They emphasized that the presence of delamination not only decreases the P cr, but also, plays an essential role in the load carrying capacity of composite structures. K¨ollner et al. [19] presented an analytical framework which allows modeling the postbuckling response of composites without such limitation. They studied the well-known problem of a composite strut with a through-the-width delamination. Their study was done up to the state of loading where the failure occurs in form of unstable delamination growth. They subjected them to buckling tests and compared them with numerical analysis results. LeBlanc and Plante [20] studied the moisture effects on delamination toughness and growth rate in a carbon/epoxy composite subjected to mixed-mode loadings. They obtained an adverse effect of moisture on delamination growth under 4
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mixed-mode loadings from the fatigue tests. Existing delamination criteria and growth rate models were evaluated to determine which ones best predict delamination toughness and growth, respectively, at any given mixed-mode ratio. Cardoso at al. [21] reported and discussed the findings from an experimental investigation on the flexural-torsional buckling behavior of pultruded glass-fiber reinforced polymer (GFRP) angle columns. A detailed material characterization was carried out and signature curves (critical load x length) were obtained using a generalized beam theory (GBT) software for predicting critical loads. In the literature, investigations on the effect of delamination on buckling load were mostly made on single delaminated composite plates. In general, studies have examined the effects of delaminations on the buckling loads. However, in a few researches, displacements in direction of plate thickness were enquired. Due to this deficiency in the literature, in this study; the effects of the delaminations size and location on buckling behaviour of the layered composites’ are inspected experimentally. As a result of buckling experiment, load-displacement graphics were obtained. The critical buckling loads were calculated by loading displacement graph. Additionally, lateral displacements were measured by transducers. Exact lateral displacement values were decided while P cr occurred. Optimum size and location of a delamination were obtained by comparison of critical buckling loads and lateral displacement values. 2. Materials and Methods
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2.1. Producing of Composite Plates and Preparation of Test Samples Material preparation phases are; composite production, curing, measuring processes, marking, cutting. 300g/m2 (0/90) E-glass fiber fabric (woven) was used as fiber reinforcement material in the production of layered composite plates. The epoxy resin (Huntsman (Araldite LY 564) epoxy and hardener mixed at a ratio of 100 : 34) was used as the matrix material. Composite plate production was carried out by resin infusion method supported with vacuum as seen in Figure 1. Eight-layered woven glass fiber reinforced epoxy resin matrix composite plates were used as materials. The reinforcing materials (woven E-glass fiber fabric) were prepared with cutting to size. The fiber fabrics are placed on the separator film so as to be centered. During placement, the first five layers are placed on top of each other, and then strips prepared from 100 microns Teflon PTFE film are placed at regular 5
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Delamination Location and Size (a/L) 5 − 6th layer / 0.3 6 − 7th layer / 0.3 7 − 8th layer / 0.3 5 − 6th layer / 0.5 6 − 7th layer / 0.5 7 − 8th layer / 0.5 5 − 6th layer / 0.7 6 − 7th layer / 0.7 7 − 8th layer / 0.7
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Sample Number A1 A2 A3 B1 B2 B3 C1 C2 C3
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Figure 1: Resin infusion method supported with vacuum
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Table 1: Sample numbers, delamination dimensions and locations in the experiments.
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intervals to provide the delaminations related with sample types. Then an upper layer of woven fabric is placed. Delamination locations were changed between 5−6th , 6−7th and 7−8th layers. In addition, delamination size with a/L ratio of 0.3, 0.5 and 0.7 rates were preferred (a: Delamination width and L: Buckling length). A total of 45 tests were performed as 5 pieces for one parameter. These sample types were given in Table 2. The sample number, the delamination dimension and the position of the delamination used in the experiments are given in Table 2. As it can be seen in Figure 2, the regions labeled ”Clamped Area” (25 mm from both sides) are reserved for the built-in fixed end of boundary conditions. The rest sample size for the buckling test was obtained as 100 mm × 30 mm × 2.3 mm. 6
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Figure 2: Buckling test specimen dimensions
Figure 3: Shimadzu AG-X with linear variable displacement transducers
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2.2. Experimental Study In the experimental study, buckling tests were carried out on a Shimadzu AG-X tensile-compressive universal test device with a load capacity of 100 kN with lateral displacement transducers as shown in Figure 3. In our tests, standard tension-compression jaws belonging to the device were used. Since the buckling test, the compression module of the device was used. These tests were carried out with a pressing speed of 1 mm/min. In the experiments, 5 specimens specially prepared for each case to be investigated were used and averages of 5 tests were taken. P cr loads were determined from the loaddisplacement graphs obtained as a result of the buckling tests made for each sample. At the end of the test, the results were recorded to the computer automatically and this data has been used in the desired graphics. Figure 12 contains force-displacement and force-lateral displacement graphs. 7
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Figure 4: Force-displacement and force-lateral displacements graph of the A1 samples
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Figure 5: Force-displacement and force-lateral displacements graph of the A2 samples
Figure 6: Force-displacement and force-lateral displacements graph of the A3 samples
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Figure 7: Force-displacement and force-lateral displacements graph of the B1 samples
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Figure 8: Force-displacement and force-lateral displacements graph of the B2 samples
Figure 9: Force-displacement and force-lateral displacements graph of the B3 samples
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Figure 10: Force-displacement and force-lateral displacements graph of the C1 samples
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Figure 11: Force-displacement and force-lateral displacements graph of the C2 samples
Figure 12: Force-displacement and force-lateral displacements graph of the C3 samples
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Figure 13: Determination of the P cr
P cr (N ) 1273 991 686
Sample Number A2 B2 C2
P cr (N ) 1260 840 655
Sample Number A3 B3 C3
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Sample Number A1 B1 C1
P cr (N ) 811 774 628
Table 2: The square mean of the experimental critical buckling loads
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Using the force-displacement graphs above, the force-displacement P cr values, which are the force values corresponding to the points at which the curve of the graph has deviated from the linearity, have been determined as shown in Figure 13. Experimental studies in the literature reference recorded to determine this point. Juh´asz at al. studied the effect of delamination on the critical buckling force of composite plates and they obtained critical buckling loads in this study. [22] The critical buckling loads found are shown in Table 2. The values in the table are the square mean of the critical buckling loads of each sample.
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3. Results and Discussion P cr - Lateral displacement comparison was made with values which obtained from the critical buckling loads given in Table 2. P cr - Lateral displacement comparison is based on the lateral displacements in millimeters corresponding to the P cr values. Comparisons were made by matching these values to each other. Figure 14 shows the case where the delamination locations are displaced from the middle interface to the upper interface while the delamination ratio is a/L = 0.3. P cr was obtained as 1273 N for A1 11
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Figure 14: Comparison of P cr and Lateral Displacement with delamination replacement between Layers (a/L = 0.3); (a) P cr Comparison, (b) Lateral Displacement Comparison
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sample. P crs were obtained as 1260 N for A2 specimen and 811 N for the A3 specimen with delamination layer position change. Decreasing rate was obtained as 36% in the P cr damage load decreases while the delamination position changed from the center interface to the edge interface. When P cr is decreasing by changing the outward position of delaminations; the opposite is obtained in the lateral displacement comparisons. It was observed that the displacements of the delamination from the middle interface to the upper interface increased lateral displacement values from 0.197 mm to 0.4 mm. The lateral displacement from the middle interface to the edge interface of the delamination affected the lateral displacement value with 103% increasing rate. Through our empirical study, we obtain that the delaminations around the mid-plane of the composite plate deteriorate the compressive instability response and hasten the buckling failure and reduce substantially the stiffness of delaminated composite plates. In Nikrad et al. [18] same results were highlighted. Hence, transfer displacement of mid-plane delaminations has less value because of hastening the buckling failure. Figure 15 shows the case where the delamination locations are displaced from the middle interface to the upper interface while the delamination ratio is a/L = 0.5. P cr was resulted as 991 N for B1 sample. P crs were obtained as 840 N for B2 specimen and 774 N for the B3 specimen with delamination layer position change. Decreasing rate was provided as 22% in the P cr damage load decreases while the delamination position changed from the center interface to the edge interface . When P cr is decreasing by changing the outward position of delami-
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Figure 15: Comparison of P cr and Lateral Displacement with delamination replacement between Layers (a/L = 0.5); (a) P cr Comparison, (b) Lateral Displacement Comparison
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nations; the opposite is found in the lateral displacement comparisons. It was observed that the displacements of the delamination from the middle interface to the upper interface increased lateral displacement values from 0.242 mm to 0.408 mm. The lateral displacement from the middle interface to the edge interface of the delamination afected the lateral displacement value with 68% increasing rate. Gong et al. [8] studied an investigation of the buckling behavior and resultant damage modes in delaminated composites subjected to four-point bending. The effect of delamination size and shape on buckling behavior was investigated using circular and elliptical delaminations in thin beams under four-point bending. They showed the orientation of the delamination had a small influence (10 − 15%) on the critical delamination-buckling load, which decreased with increasing ratio of minor to major axis length of the delamination. Small delamination has no big influence on the failure mode of the composite laminate. As might be expected, the P cr decreased with increasing size of the delamination. Figure 16 shows the case where the delamination locations are displaced from the middle interface to the upper interface while the delamination ratio is a / L = 0.7. The maximum P cr was obtained as 686 N for C1 sample. P crs were obtained as 655 N for C2 specimen and 628 N for the C3 specimen with delamination layer position change. Decreasing rate was obtained as 8% in the P cr damage load decreases while the delamination position changed from the center interface to the edge interface. When P cr is decreasing by changing the outward position of delamina13
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Figure 16: Comparison of P cr and Lateral Displacement with delamination replacement between Layers (a/L = 0.7); (a) P cr Comparison, (b) Lateral Displacement Comparison
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Figure 17: Damage loads and lateral displacements in delamination size increase between 7th and 8th layers; (a) P cr Comparison, (b) Lateral Displacement Comparison
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tions; the opposite is performed in the lateral displacement comparisons. It was observed that the displacements of the delamination from the middle interface to the upper interface increased lateral displacement values from 0.25 mm to 0.588 mm. The lateral displacement from the middle interface to the edge interface of the delamination affected the lateral displacement value with 135% increasing rate. Short et al. [5] showed that a delamination near the outside of the curve gave a greater strength reduction than a delamination near the inside of the curve, where both delaminations were at the same depth in their study like this study. In Figure 17, P cr and lateral displacement comparisons are given with the increase of the delamination rate in the same layer. The maximum
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Figure 18: Damage loads and lateral displacements in delamination size increase between 6th and 7th layers; (a) P cr Comparison, (b) Lateral Displacement Comparison
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P cr was carried out as 811 N for A3 sample. P crs were achieved as 774 N for B3 specimen and 628 N for the C3 specimen with the increase of the delamination rate in the same layer. Decreasing rate was obtained as 22% in the P cr damage load decreases while the delamination position shifted from the middle interface to the edge interface. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. Lateral displacements measured as 0.4 mm for A3, as 0.408 for B3, as 0.588 for C3. It was observed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 47% increasing rate. In Figure 18, P cr and lateral displacement comparisons are given with the increase of the delamination rate in the same layer. The maximum P cr was performed as 1260 N for A2 sample. P crs were obtained as 840 N for B2 specimen and 655 N for the C2 specimen with the increase of the delamination rate in the same layer. Decreasing rate was obtained as 48% in the P cr damage load decreases while the delamination position shifted from the middle interface to the edge interface. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. Lateral displacements measured as 0.324 mm for A2, as 0.326 for B2, as 0.348 for C2. It was viewed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 7% increasing rate. In Figure 19, P cr and lateral displacement comparisons are given with the increase of the delamination rate in the same layer. The maximum P cr was found as 1273 N for A1 sample. P crs were seen as 991 N for B1 specimen and 686 N for the C1 specimen
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Figure 19: Damage loads and lateral displacements in delamination size increase between 5th and 6th layers; (a) P cr Comparison, (b) Lateral Displacement Comparison
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with the increase of the delamination rate in the same layer. Decreasing rate was 46% in the P cr damage load decreases while the delamination position shifted from the middle interface to the edge interface. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. Lateral displacements measured as 0.197 mm for A1, as 0.242 mm for B1, as 0.25 mm for C1. It was observed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 26% increasing rate. Gu and Chattopadhyay [3] obtained both the critical stress and the ultimate stress reduced as the delamination length increases. They obtained the same size delamination position change from center lay to surface face decreased P cr. Lateral deflection measured to get buckling points. 4. Conclusion
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In this study, the effect of delamination size and location to P cr and lateral displacement behavior of composite materials was investigated. The remarkable results obtained from experiments are presented below. 1. The increase in delamination size on the same layer decreased the critical buckling loads. 5−6th layer, 6−7th layer and 7−8th layer decreasing rate was obtained as 46%, 48% and 22% respectively in the P cr failure load decreases while the increase in delamination size on the same layer.
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2. Delaminations of the same size reduced the buckling loads by changing the position from the middle interface to the upper interface. 5 − 6th layer, 6 − 7th layer and 7 − 8th layer decreasing rate was obtained as 36%, 22% and 08% respectively while the P cr damage load decreases by changing the position from the middle interface to the upper interface. 3. The increase in delamination size on the same layer increased the lateral displacements corresponding to the buckling loads of the material. While the increase of the delamination rate in the same layer, P cr decreased but lateral displacement increased. It was observed that the size rate increasing of the delamination from 0.3 to 0.7; lateral displacement rate changed with 26% increasing rate. 4. The location of the delaminations from the middle interface to the upper interface increased lateral displacements corresponding to buckling loads. The lateral displacement from the middle interface to the edge interface of the delamination affected the lateral displacement value with 135%, 68% and 103% increasing rate respectively for a / L = 0.3, 0.5 and 0.7.
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[1] Kim, Y., Davalos,J., Barbero, E.,( 1997) Delamination buckling of FRP layer in laminated wood beams, Composite Structures Vol. 37, No. 314, pp. 311-320. [2] Hyo-Jin, K. ve Chang-Sun, H., (1997). Buckling and post buckling behavior of composite laminates with a delamination. Composites Science and Technology, 57: 557-564.
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[3] Gu, H., Chattopadhyay, A., An experimental investigation of delamination buckling and postbuckling of composite laminates, Composites Science and Technology 59 (1999) 903-910. [4] Hwang, S. ve Liu, G., (2001). Buckling behavior of composite laminates with multiple delaminastions under uniaxial compression. Composite Structures, 53: 235-243. [5] Short, G., Guild, F., Pavier, M., Delaminations in flat and curved composite laminates subjected to compressive load, Composite Structures 58 (2002) 249258.
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[6] Arman, Y., Zor, M., Aksoy, S., Determination of critical delamination diameter of laminated composite plates under buckling loads. Composites Science and Technology 66 (2006) 29452953. [7] Cappello, F. ve Tumino, D., (2006). Numerical analysis of composite plates with multiple delaminations subjected to uniaxial buckling load. Composites Science and Technology, 66: 264-72.
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[8] Gong, W., Chen, J., Patterson, E., An experimental study of the behaviour of delaminations in composite panels subjected to bending, Composite Structures 123 (2015) 918.
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[9] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Local buckling behavior of FRP thin-walled beams: A mechanical model, Composite Structures 98 (2013) 111-120. [10] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Buckling failure modes of FRP thin-walled beams: A mechanical model, Composites: Part B 47 (2013) 357-364.
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[11] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Macro-scale analysis of local and global buckling behaviorof T and C composite sections, Mechanics Research Communications 58 (2014) 105-111.
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[12] Ruan, J. T., Aymerich, F., Tong, J. W. and Wang, Z. Y., (2014). Optical evaluation on delamination buckling of composite laminate with mpact damage, Advances in Materials Science and Engineering, Volume 2014, Article ID 390965.
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[13] Ascione, L., Berardi, V.P., Giordano, A., Spadea, S., Pre-buckling imperfection sensitivity of pultruded FRP profiles, Composites: Part B 72 (2015) 206212. [14] Juh´asz, Z. And Szekr´enyes, A., (2015). Estimation of local delamination buckling in orthotropic composite plates using kirchhoff plate finite elements, Mathematical Problems in Engineering, Volume 2015, Article ID 749607. [15] Ahna, D.,Choib, J., and Kweonb, J., Relationship between the drilling condition and the damage (delamination) zone of glass-fiber-reinforced
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plastic composites, Advanced Composite Materials, 2015, Vol. 24, No. 3, 297305. [16] Pernice, M., Carvalho, N., Ratcliffe, J., Hallett, S., Experimental study on delamination migration in composite laminates, Composites: Part A 73 (2015) 2034.
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[17] Kharghani, N., Soares, C., Behavior of composite laminates with embedded delaminations, Composite Structures 150 (2016) 226239.
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[18] Nikrad, S., Keypoursangsari, S., Asadi, H., Akbarzadeh, A., Chen, Z., Computational study on compressive instability of composite plates with off-center delaminations, ScienceDirect, Comput. Methods Appl. Mech. Engrg. 310 (2016) 429459. [19] K¨ollner, A., Jungnickel, R., and V¨ollmecke, C., (2016). Delamination growth in buckled composite struts, Springer Science+Business Media Dordrecht, Int J Fract (2016) 202:261269.
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[20] LeBlanc, L. and LaPlante, G., Experimental investigation and finite element modeling of mixed-mode delamination in a moisture-exposed carbon/epoxy composite, Composites: Part A 81 (2016) 202213. [21] Cardoso, D.C.T., Togashi, B.S., Experimental investigation on the flexural-torsional buckling behavior of pultruded GFRP angle columns, Thin-Walled Structures 125 (2018) 269-280.
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[22] Juh´asz, Z. And Szekr´enyes, A., The effect of delamination on the critical buckling force of composite plates: Experiment and simulation, Composite Structures 168 (2017) 456464.
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